Question: Simplify to lowest terms. $\dfrac{110}{44}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 110 and 44? $110 = 2\cdot5\cdot11$ $44 = 2\cdot2\cdot11$ $\mbox{GCD}(110, 44) = 2\cdot11 = 22$ $\dfrac{110}{44} = \dfrac{5 \cdot 22}{ 2\cdot 22}$ $\hphantom{\dfrac{110}{44}} = \dfrac{5}{2} \cdot \dfrac{22}{22}$ $\hphantom{\dfrac{110}{44}} = \dfrac{5}{2} \cdot 1$ $\hphantom{\dfrac{110}{44}} = \dfrac{5}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{110}{44}= \dfrac{2\cdot55}{2\cdot22}= \dfrac{2\cdot 11\cdot5}{2\cdot 11\cdot2}= \dfrac{5}{2}$